Question

Two coherent light sources $A$ and $B$ are at a distance $3\lambda$ from each other $(\lambda =$ wavelength $)$. The distance from $A$ on the $+X$-axis at which the first constructive interference is found to be $N\lambda$. What is the value of $N$ ?

Answer 1

Answer: 4

Let $P$ be the point on $X$-axis, where constructive interference is obtained and $AP$ be $x$.

For first constructive interference,
$BP-AP=\lambda$
Further, $\sqrt{9{\lambda }^2+x^2}-x=\lambda$
$\therefore 9{\lambda }^2+x^2=x^2+{\lambda }^2+2x\lambda$
$x=4\lambda$